BOAO, China—The U.S. is telling China's $500 billion sovereign-wealth fund to "go away," according to the fund's top executive, in the latest sign of strained investment ties between the world's two largest economies.

During the financial crisis, "we were sort of welcome" in America, said Gao Xiqing, head of China Investment Corp., in a panel discussion on Sunday at the Boao Forum for Asia. Since then, "somehow we've become stigmatized," he said, adding that "there have been quite a few cases...